Can Rabbits Dig Out?

I have a 4 year old, female, mixed breed rabbit. She's in a raised enclosure witch is inside a pen. I took a picture to give you a better idea.
Anyway, I was thinking of making her another hutch directly on the ground. It's already mostly built, I just need to add a shelter and gate. It would be mobile so she could have fresh grass every week or so, and it would be a lot less cleaning for me. The only two things that concern me are...
1. Theres no bottom. Could she dig out? She's never been on the ground without my supervision for long so I don't know if she would try. If she does... well, I have a dog who would love her for dinner. Which brings me to...
2. I don't trust my dog with her on the ground. My thought here was to put her in my goat pen where there is plenty of grass because they don't eat it much. (They are two Pygmies) However, being goats, they will likely walk on top of her cage. Will that stress her out? The goats use to be in the pen that contained her other cage. So, she is very used to seeing and hearing them, them chewing on her gates, and trying to get to her food. Anyone with more experience have any thoughts, opinions, advice? Thanks in advance.

You could just stack hay / straw bales on top of the hutch and then cover it with tarpaulin to prevent it from spoiling

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That's actually a good idea. So even if the goats got on the hay it wouldn't be noisy. It would also help her feel more secure, and not out in the open. I would probably use already spoiled, or scrap hay so I wouldn't have to worry about covering it. Thank you.